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Question

Tangents are drawn from different points on the line xy+10=0 to the parabola y2=4x. If the chords of contact pass through a fixed point, then the coordinates of the fixed point is

A
(2,5)
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B
(5,2)
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C
(10,2)
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D
(2,10)
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Solution

The correct option is C (10,2)
Let any point on the line
xy+10=0 be (t,t+10)
From this point, the equation of chord of contact to the parabola y2=4x is,
T=0
y(t+10)=2(x+t)
2x10y+t(2y)=0
So, the fixed point is the intersection of line,
2x10y=0 & 2y=0
y=2x=10

Hence, the fixed point is (10,2)


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